Refers to a person whose job is cooking, especially in a professional kitchen. Similar to 料理人, but 料理番 can carry a slightly older or more specific nuance of being assigned to cooking duties.
See also: 料理人
He works as a cook at a French restaurant.
The cook at the inn starts preparations early in the morning.
Compound of 料理 (cooking) and 番 (watch, duty, person in charge). The exact historical derivation is uncertain, but it follows a common pattern for occupational terms.